This note aims to give an application of entropy to the analysis of algorithms, using Shearer’s entropy lemma to bound the running time of Bellman’s dynamic programming solution to the traveling salesman problem. The original venue for this material was my course Randommised algorithms (2008) at Lund University. 1. The Traveling Salesman Problem Given a weighted graph like

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa–Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied. 2005 Elsevier Ltd. All rights reserved.

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows. This result is then extended to the cases of periodic habitat and weak compactness, respectively. We also apply the developed theory to four classes of evoluti...

We numerically simulate the traveling time of a tracer in convective flow between two points (injection and extraction) separated by a distance r in a model of porous media, d=2 percolation. We calculate and analyze the traveling time probability density function for two values of the fraction of connecting bonds p: the homogeneous case p=1 and the inhomogeneous critical threshold case p=p(c). ...

An Eflective Heuristic Algorithm for the Traveling. THE SYMMETRIC traveling-salesman problem is: Given an n by n symmetric matrix of.symmetric traveling salesman problem. However, the design and implementation of an algorithm based on this heuristic is not trivial. There are many.This article is about the heuristic for the travelling salesman problem. An Effective Heuristic Algorithm for the Tr...

We present a genetic algorithm for solving the traveling salesman problem by genetic algorithms to optimality for traveling salesman problems with up to 442 cities. Mlihlenbein et al. [MGK 88], [MK 89] have proposed a genetic algorithm for the traveling salesman problem, which generates very good but not optimal solutions for traveling salesman problems with 442 and 531 cities. We have improved...

It is a long time that the Simulated Annealing (SA) procedure has been introduced as a model-free optimization for solving NP-hard problems. Improvements from the standard SA in the recent decade mostly concentrate on combining its original algorithm with some heuristic methods. These modifications are rarely happened to the initial condition selection methods from which the annealing schedules...

While it was known for a long time how to transform an asymmetric traveling salesman problem on the complete graph with n vertices into a symmetric traveling salesman problem on an incomplete graph with 2n vertices, no method was available until recently for using this correspondence to derive facets of the symmetric traveling salesman polytope from facets of the asymmetric one. In this paper w...

Transmission lines are designed to transfer electric power from source locations to distribution networks. This project investigates the problem of fault localization using traveling wave voltage and current signals obtained at a single end of a transmission line and multi ends of a transmission network. Fourier transform (FT) is the most popular transformation that can be applied to traveling ...

Traveling-wave-based fault location in electrical distribution systems is an important safeguard for the distribution network reliability. The effectiveness of the methods is verified directly in power grid in the early stages, while different fault types can't appear in a short time. And normal dynamic physical simulation cannot meet the teaching demand either because of the limitation of tran...